Bialgebras, and Lie monoid actions in Morse and Floer theory, I
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908346767900672 |
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| author | Cazassus, Guillem Hock, Alexander Mazuir, Thibaut |
| author_facet | Cazassus, Guillem Hock, Alexander Mazuir, Thibaut |
| contents | We introduce a new family of oriented manifolds with boundaries called the forest biassociahedra and forest bimultiplihedra, generalizing the standard biassociahedra. They are defined as moduli spaces of ascending-descending biforests and are expected to act as parameter spaces for operations defined on Morse and Floer chains in the context of compact Lie group actions.
We study the structure of their boundary, and derive some algebraic notions of ``$f$-bialgebras'', as well as related notions of bimodules, morphisms and categories. This allows us to state some conjectures describing compact Lie group actions on Morse and Floer chains, and on Fukaya categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16225 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bialgebras, and Lie monoid actions in Morse and Floer theory, I Cazassus, Guillem Hock, Alexander Mazuir, Thibaut Symplectic Geometry Combinatorics Category Theory Geometric Topology Quantum Algebra We introduce a new family of oriented manifolds with boundaries called the forest biassociahedra and forest bimultiplihedra, generalizing the standard biassociahedra. They are defined as moduli spaces of ascending-descending biforests and are expected to act as parameter spaces for operations defined on Morse and Floer chains in the context of compact Lie group actions. We study the structure of their boundary, and derive some algebraic notions of ``$f$-bialgebras'', as well as related notions of bimodules, morphisms and categories. This allows us to state some conjectures describing compact Lie group actions on Morse and Floer chains, and on Fukaya categories. |
| title | Bialgebras, and Lie monoid actions in Morse and Floer theory, I |
| topic | Symplectic Geometry Combinatorics Category Theory Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2410.16225 |